The value of the b quark mass at the MZ scale defined in the View the MathML source renormalization scheme, mb(MZ), was determined using 2.8 million hadronic Z decays collected during 1992-1994 by the DELPHI detector to be View the MathML source The analysis considers NLO corrections to the three-jet production rate including mass effects, and the result obtained agrees with the QCD prediction of having a running b quark mass at an energy scale equal to MZ. This is the first time that such a measurement is performed far above the View the MathML source production threshold. The study also verifies the flavour independence of the strong coupling constant for b and light quarks within 1% accuracy.